One of the major steps in the development of a systematic design methodology for the creative design of vehicle mechanisms is to obtain all possible link assortments, and then to generate the catalogs of kinematic chains. If the generalized mathematical expressions for the maximum value M of the maximum number of joints incident to a link of kinematic chains with N links and J joints can be derived, the process of solving link assortments can be more systematic. Using elementary concepts of graph theory, we derived explicit relationships for M for two regions of the J-N plane.

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